James Rodriguez celebrates after scoring during the World Cup. Photo: Reuters

Spanish sports newspaper As said on Monday that Monaco had agreed terms with Madrid, whose president Florentino Perez had delayed his flight to Los Angeles where the club's squad has some pre-season training.

Sports newspaper Marca, traditionally very close to Madrid's boardroom, said Rodriguez is to be presented to fans on Tuesday.

Marca and As said Madrid had agreed with Monaco a price of 80 million euros ($A120 million) for Rodriguez, and that the player would join the squad on the first day of August.

Madrid has already signed Germany midfielder Toni Kroos for next season.

Both Kroos and Rodriguez could play in the European Super Cup against Sevilla in Cardiff on August 12.

As said Rodriguez had made a brief stop-over in Madrid on Sunday and was spotted arriving back at the city's international airport on Monday morning.